The invention relates to a method of deriving geometrical data of a structure from an image of the structure, in which
marker points are selected in the image,
a typical contour is associated with the marker points, and
geometrical data is calculated from the typical contour.
The invention also relates to a data processor which is arranged to carry out such a method.
A method of this kind is known from the article xe2x80x9cDigital radiography segmentation of scoliotic vertebral body using deformable modelsxe2x80x9d, published in SPIE Vol. 3034, 1997.
The known method is intended notably for deriving the degree of deformation, relative to a healthy spinal column, from an image of a spinal column of a patient to be examined. According to the known method, every vertebra is approximately by a deformed standard template. The templates are slightly rounded trapezia having dimensions which correspond to statistically mean dimensions of the respective vertebrae. Such a statistical mean value is determined from the dimensions of the vertebrae of a large number of patients having a spinal column deformed by scoliosis. The respective standard templates are deformed by scaling the height and the individual parallel sides in order to make them correspond as well as possible to the relevant vertebrae in the image. The standard templates are characterized by their height and a number of scale variables. The dimensions of the sides of the standard templates and the radius of curvature of concave sides of the standard templates are respective products of the height and one of the scale variables. Separate values of the height and the scale variables exist for different vertebrae. The known method thus takes into account the fact that the spinal column comprises vertebrae having different shapes and dimensions. The values of the scale variables have been estimated on the basis of data known from literature. The values for the heights have been derived from a large number of X-ray images of scoliotic patients. The typical contour corresponding to the edge of the spinal column in the image is derived from the standard templates. Furthermore, specific positions are indicated on the derived typical contour. A three-dimensional reconstruction of the imaged spinal column is carried out on the basis of said specific positions.
In order to carry out the known method it is necessary to determine characteristic dimensions of a large number of vertebrae in spinal columns of a large number of patients so as to form the standard templates. In order to make the standard templates correspond to the vertebrae in the image, the central axis of the spinal column is estimated by looking and a number of marker points is indicated on the estimated central axis. The central axis is subsequently approximated by a cubic curve through the indicated marker points on the central axis. Subsequently, the standard templates are deformed in such a manner that they are distributed as well as possible along the cubic curve. This makes the known method rather cumbersome. Because the known method utilizes standard templates relating to an average spinal column suffering from scoliosis, the known method is not very well suitable for accurately deriving spatial geometrical data relating to a spinal column exhibiting serious anomalies.
Notably when the image concerns an X-ray image of the spinal column it often occurs that a part of the marker points is not visible. The contrast of the vertebrae reproduced in an X-ray image often is not sufficient to see the marker points. Even if all marker points are visible in the X-ray image, usually not all of them are visible clearly enough to enable accurate indication of their position in the image.
It is an object of the invention to provide a method of deriving geometrical data of a structure from an image of the relevant structure which is less cumbersome than the known method and, moreover, enables more accurate results to be obtained.
This object is achieved by means of a method of deriving geometrical data of a structure from an image of the relevant structure according to the invention which is characterized in that
correctness values are associated with the marker points,
a cost function is associated with the typical contour,
which cost function is dependent on the shape of the typical contour and on the values of the correctness values, and
which typical contour is chosen in such a manner that the cost function has an optimum value.
For each of the selected marker points the correctness values represent the likelihood that the selected marker point accurately corresponds to a typical anatomical detail of the structure. The use of the method according to the invention notably concerns the determination of spatial geometrical data of the spinal column of a patient to be examined. In this application the marker points are selected to be situated at the positions in the image which correspond to the corner points of the vertebrae and to anatomically typical points at the edges of the relevant vertebral body. It appears that the marker points are not always suitably visibly reproduced in the image; this occurs notably when the image is an X-ray image of the spinal column. It is to be noted, however, that the marker points are not always clearly visible either in, for example magnetic resonance images of the spinal column. By associating the typical contour with the marker points the method according to the invention takes into account that the fact that not all marker points correspond equally accurately to the relevant positions in the spinal column. Upon association of the typical contour the value of the cost function is calculated and the typical contour is determined in such a manner that the cost function has an optimum value. The cost function is dependent on the correctness values of the marker points. It is thus achieved that the typical contour for which the cost function is optimized is determined predominantly by marker points having a high correctness value, i.e. by marker points for which it is rather certain that they accurately correspond to their relevant anatomically typical positions in the structure, such as the spinal column. The typical contour accurately corresponds with the boundary of the structure at issue in the image. Often, such a typical contour is a closed loop, e.g. when the structure is a vertebra. The typical contour may also comprise separate disconnected curves or straight line portions. For example, the correctness value of individual marker points is dependent on the differences between the brightness value in the marker point and brightness values in positions in the image in the vicinity of the relevant marker point. Generally speaking, suitable marker points correspond to anatomically typical positions; in that case differences between the brightness value in the relevant marker point and in individual directions adjacent the relevant marker point have values which are more or less predetermined. For example, such differences occur when the marker point is situated at the corner of a bone, such as a vertebra, which is surrounded by softer and less dense tissue, such as muscular tissue or lung tissue. The better the correspondence between such differences in the image and the predetermined differences, the higher the likelihood of accurate correspondence between the relevant marker point and the corresponding typical anatomical position. Therefore, the correctness values are preferably dependent on the predetermined differences or gradients in separate directions of brightness values in the vicinity of the relevant marker point. Marker points for which it is uncertain whether they correspond to their relevant anatomical position have a comparatively small effect only on the typical contour. Because the cost function is also dependent on the shape of the typical contour, it is achieved that the association of a typical contour having improbable shapes is counteracted and that, conversely, the association of a typical contour having expected, frequently occurring shapes is favored. For example, the cost function is chosen in such a manner that a high value of the cost function is associated with typical contours where the direction of the typical contour abruptly changes in many locations.
In the context of the method according to the invention the optimum value of the cost function is to be understood to mean the value of the cost function associated with a typical contour which accurately represents the geometry of the relevant structure. This means that the typical contour is formed in such a manner that for a curve which is associated with the marker points but deviates from the typical contour, the value of the cost function is, for example higher or lower than the optimum value; the optimum value is in that case a (local) maximum or a (local) minimum, respectively.
Using the method according to the invention it is achieved that the typical contour accurately represents the spatial geometry of the structure, notably the spinal column of the patient to be examined. The typical contour is, for example a curve through the centers of the successive vertebrae. The typical contour may also represent the edge of the spinal column. The course in space of the spinal column of the patient to be examined can be derived from the variation of the typical contour. This course in space is represented notably by the values of a small number of so-called Cobb angles and the mutual orientations of the individual vertebral bodies. The Cobb angles are the angles enclosed by the upper side and the lower side of respective vertebrae relative to one another. The Cobb angles of individual pairs of vertebrae offer an accurate indication of the three-dimensional shape of the spinal column. It has been found notably that the method according to the invention is a suitable technical aid for accurately following the development of deformations, as caused by scoliosis, of the spinal column of the patient to be examined. The invention is also suitable for deriving the geometrical data of the rib cage of the patient to be examined.
These and other aspects of the invention will be elaborated on the basis of the following embodiments which are defined in the dependent claims.
Preferably, according to the invention first a number of marker points is indicated by hand. Among all relevant marker points there are usually a number which are clearly visible in the image. Such clearly visible marker points can be readily indicated by hand. Such indications can be realized, for example by displaying the image on a monitor of a workstation and by indicating the marker points by means of a cursor, the position of the cursor upon indication of the respective marker points being stored. The marker points can also be indicated by touching them on the display screen of the monitor by means of a pointer and by storing the positions of the points where the display screen is touched by the pointer. The marker points can also be indicated by indicating these points on a radiological film by means of a digitizer. It has been found that in many situations the positions of marker points which are not or only poorly visible in the image can be derived from the indicated marker points. It is notably when the structure whereto the image relates has been determined in advance that it is usually possible to derive from indicated marker points other marker points which are situated therebetween. To this end, it is merely necessary to indicate the most clearly visible marker points and the user need not make the effort of searching poorly visible marker points in the image. It is notably when the image concerns a periodic structure that the derived marker points can be found very well on the basis of the indicated marker points. The positions of the derived marker points can be simply found by interpolation between the positions of the indicated marker points. It is notably when the image concerns a periodic structure that very accurate results are obtained by way of interpolation.
The imaged structure may be of a rather complex spatial shape; the imaged structure may notably comprise a plurality of sectors. Some of these sectors are suitably visible in the image whereas other sectors are much more difficult to distinguish. In such a situation it is handy to indicate the indicated marker points only in the indicated sectors. The derived marker points in the derived sectors can be derived from the indicated marker points in the indicated sectors. The derived sectors may be, for example difficult to distinguish in the image. Because the number of sectors and, for example, also the periodicity of the succession of sectors of the structure are usually known, indicated and derived marker points can be readily determined in all indicated and derived sectors. Overlooking of sectors can be easily avoided by ensuring that the derived marker points are chosen in such a manner that, in conjunction with the indicated marker points, they represent the already known number of sectors with the correct periodicity. It is also possible to save time by manually indicating the indicated marker points in only a small number of indicated sectors. If the image concerns a spinal column, the sectors relate to individual vertebrae.
The typical contour preferably represents the central axis of the structure. It is notably when the image structure has an elongate shape that the central axis indicates predominantly the spatial orientations of individual parts of the structure relative to one another. It is particularly advantageous to take the central axis of the spinal column of the patient to be examined as the typical contour. The central axis then accurately indicates the orientations of the individual (groups of) vertebrae relative to one another. It has been found that the central axis of the spinal column can be accurately derived by plotting a smooth curve, such as a poly-Bezier curve, a cubic curve or a spline curve, through a small number of derived marker points. Such derived marker points are preferably taken for successive vertebrae, each time halfway between two marker points at oppositely situated corner points of one and the same vertebra.
Another typical contour represents an edge of the imaged structure. This typical contour may comprise a plurality of parts, each of which represents a separate edge of the imaged structure. The typical contour representing such an edge of the structure can be accurately determined, inter alia on the basis of gradients or differences between brightness values in the image. The differences between brightness values to both sides of such an edge is usually much larger than those within or outside the imaged structure. The typical contour representing an edge of the imaged structure may also relate to the edges of individual sectors. Such a typical contour representing an edge in the image is preferably derived from a gradient image of the image. Such a gradient image contains differences between brightness values in neighboring positions in the image of the structure. The gradient image preferably also contains the direction of the brightness gradients in the image. This means that the gradient image associates the vector (magnitude and direction) of the brightness gradient with different positions in the image. The cost function of the typical contour is chosen in such a manner that curves along which large brightness gradients occur in the gradient image, for example in a predetermined direction, are strongly favored in the image.
In many cases the approximate angle enclosed by an edge of a sector relative to the central axis of the structure is known in advance. For example, edges of individual vertebrae extend transversely of the central axis of the spinal column. In order to facilitate the search for the edges of the individual sectors, use is made of a cost function which associates optimum values with typical contours along positions having large brightness gradients in the direction which corresponds to the already known angle relative to the central axis. A suitable cost function is, for example dependent on the scalar product of the brightness gradient and the directional vector along the typical contour.